Stories sometimes have a way of making themselves true. The notion of The Rolling Stones as the “bad boys” of British ’60s rock, for instance, may have had a basis in reality and personality, but it also originated as a term of marketing and media shorthand. As Brett Morgen’s new HBO documentary Crossfire Hurricane (premieres tonight, Nov. 15) notes early on, as the Stones began to break out after The Beatles’ success, the press framed their narrative as the villains to the Beatles’ nice guys, the satisfaction-getters vs. the hand-holders.

It may have been a story, but it was one that the Stones readily enough embodied. They got big fast, they provoked and aroused millions, they were touched by drugs and eventually death. Like The Beatles, though, they also demonstrated an artistry, depth and ability to grow beyond the one-note media story of their early success. Just as The Beatles went from moptops writing simple pop songs to global experimentalists, the Stones went from straightforward blues rebellion to creating a kind of poetry of self-destruction, peaking with work like Exile on Main Street.

Crossfire Hurricane uses documentary outtake footage from decades of earlier films to spin a new take on that trip, paralleling the Stones as news story (the drug busts, Brian Jones’ death, Altamont) to their development as artists, aiming to show how one was inseparable from the other. It’s not a movie for music geeks, in the sense of unpacking the band’s influences or closely analyzing how their songs worked. Instead it links the music to the members’ stories, trying to capture how the electricity of the group’s personalities created art. It’s not a revelation, but it’s an intimate story of the band, with performance sequences that show how five guys—in different lineups—came together and made an entity of pure fire and sex.

Timed for the band’s 50th anniversary, Crossfire Hurricane aims to be, to take a quote from Mick Jagger, the story of the band’s transformation from “the band everybody hated to the band everybody loves.” The funny thing about the Stones’ story is that it includes about twenty years of turbulence and brilliance, then another thirty of stability, belovedness and (relative) creative dormancy. The first part is the more immediately interesting, so it’s not surprising that Crossfire Hurricane focuses almost entirely on the ’60s and ’70s. Still, it would be interesting to see the documentary Morgen, or someone else, could make concentrating on what it means to be an established band settling in for three decades of playing the hits. Maybe some day we’ll get one for an encore.